Answer
9 songs
Work Step by Step
Janis's willingness to pay per song decreases by \$1 for each additional song:
1st song: \$9
2nd song: \$8
3rd song: \$7
4th song: \$6
5th song: \$5
6th song: \$4
7th song: \$3
8th song: \$2
9th song: \$1
10th song: \$0
Since songs are free, Janis will play 9 songs, stopping when her marginal benefit reaches zero.
Plot WTP on the vertical axis vs number of songs on the horizontal axis. Price = \$0 is a horizontal line. All songs with WTP above \$0 are chosen.
